Actually many chemicals rapidly break down in an aqueous solution. I don't know specifics about chlorhexidine, but its not that uncommon.
I mix up a new batch everytime I clean. I got a gallon of the concentrate which = 128 gallons or working solution. I just mix up enough for a spray bottle's worth, I've had that gallon a couple of years, and its barely 1/4 of the way down. So far worth every penny I spent on it.
I figure its better safe than sorry, and with it being so cheap, no reason not to.